Screw machines, whether this be in the form of screw compressors or in the form of screw expanders, have been in practical use for several decades. Configured as screw compressors, they have superseded reciprocating piston compressors as compressors in many areas. With the principle of the intermeshing pair of screws, not only gases can be compressed by applying a certain amount of work. The application as a vacuum pump also opens up the use of screw machines to achieve a vacuum. Finally an amount of work can also be produced by passing through pressurized gases the other way round so that mechanical energy can also be obtained from pressurized gases by means of the principle of the screw machine.
Screw machines generally have two shafts arranged parallel to one another on which a main rotor on the one hand and a secondary rotor on the other hand are located. Main rotor and secondary rotor intermesh with a corresponding screw-shaped toothed structure. Between the toothed structures and a compressor housing which accommodates the main and secondary rotor, a compression chamber (working chambers) is formed by the tooth gap volumes. Starting from a suction region as the rotation of main and secondary rotor progresses, the working chamber is initially closed and then continuously reduced in volume so that a compression of the medium occurs. Finally as rotation progresses, the working chamber is opened towards a pressure window and the medium is expelled into the pressure window. Screw machines configured as screw compressors differ by this process of internal compression from Roots blowers which operate without internal compression.
Depending on the required pressure ratio (ratio of output pressure to input pressure), various tooth number ratios are appropriate for efficient compression.
Typical pressure ratios can be between 1.1 and 20 depending on the tooth number ratio, where the pressure ratio is the ratio of compression end pressure to suction pressure. The compression can take place in a single- or multistage manner Attainable final pressures can, for example, lie in the range of 1.1 bar to 20 bar. Insofar as at this point or hereinafter in the present application reference is made to pressure information in “bar”, in each case this pressure information relates to absolute pressures.
In addition to the already mentioned function as a vacuum pump or as a screw expander, screw machines can be used in various areas of technology as compressors. A particularly preferred area of application is the compression of gases such as, for example, air or inert gases (helium, nitrogen, . . . ). However, it is also possible, although this imposes especially structurally different requirements, to use a screw machine to compress refrigerants, for example for air-conditioning systems or refrigeration applications. For the compression of gases specifically with higher pressure ratios, usually a fluid-injected compression, in particular an oil-injected compression is used; however it is also possible to operate a screw machine according to the principle of dry compression. In the lower-pressure area, screw compressors are occasionally also designated as screw blowers.
Over the past few decades, considerable success has been achieved in regard to the manufacturability, reliability, smooth running and efficiency of screw machines. Improvements or optimizations in this context frequently relate to optimizations of the efficiency depending on number of teeth, wrap-around angle and length/diameter ratio of the rotors. The incorporation of the transverse sections in the optimization process has only taken place recently.
Experiments have shown that the transverse section of the rotors, in particular the transverse section of the secondary rotor has a substantial influence on the energy efficiency. In order to obey the toothed structure laws, the transverse section of the secondary rotor must find its correspondence in the transverse section of the main rotor. The profile of the rotor in a plane perpendicular to the axis of the rotor is here designated as transverse section. Various types of transverse section generation such as, for example, rotor- or rack-based transverse section generating methods are now known from the prior art. If a specific process has been decided upon, a first draft transverse section is generated in a first step. This is conventionally further optimized in a plurality of successive (revising) steps according to various criteria.
Here both the optimization aims per se (energy efficiency, smooth running, low costs) and also the fact that the improvements of one parameter in some cases necessarily result in a deterioration of another parameter, are known. However, there is a lack of a specific solution as to how a good overall optimization result (i.e. a compromise between the various individual parameter optimizations) can be achieved.
Some optimization approaches which are known in the prior art with a view to improving the energy efficiency, smooth running and costs will be explained as an example hereinafter. Furthermore, problems which can arise here will also be mentioned.
1 Energy Efficiency
The energy efficiency of compressor blocks can advantageously be influenced in a known manner by minimizing the internal leakages in the compressor block and in particular by reducing the gap between main rotor and secondary rotor. Specifically here a distinction should be made between the profile gap and the blow hole:                Via the profile gap the pressure-side working chambers have direct communication to the suction side and therefore the greatest possible pressure difference for backflows.        Consecutive working chambers are interconnected via a theoretically unnecessary passage which is designated as blow hole. In some cases this is also designated as head rounding opening. This blow hole is obtained through the head rounding of the profiles, in particular the profile of the secondary rotor. Pressure-side working chambers are connected to the respectively adjacent working chamber via pressure-side blow holes, suction-side working chambers are connected to the respectively adjacent working chambers via suction-side blow holes. Unless specified otherwise, the term “blow hole” is to be understood hereinafter as “pressure-side blow hole”.        
Ideally, in order to minimize internal leakages, a short profile gap length should be combined with a small (pressure-side) blow hole. However, the two quantities behave fundamentally contrarily. That is, the smaller the blow hole is modelled, the larger the profile gap length must be. Conversely, the blow hole becomes larger, the shorter is the profile gap length. This is explained, for example, by Helpertz in his dissertation “Method for the stochastic optimization of screw rotor profiles”, Dortmund, 2003, on page 162.
The requirement for a short profile gap length can be achieved in a known manner with a flat profile with a relatively small relative profile depth of the secondary rotor. Whether a profile is designed to be rather flat (small profile depth) or deep (large profile depth) can be clearly quantified here by means of the so-called “relative profile depth of the secondary rotor” which relates the difference between addendum and dedendum circle radius to the addendum circle radius of the secondary rotor. The higher is the value, the more compact is the compressor block and for example, has more quantity delivered than a comparable compressor block with the same external dimensions.
Profiles designed to be very flat accordingly have a poor utilization of installation volume, i.e. they result in large compressor blocks with comparatively high material expenditure or comparatively high manufacturing costs.
Pressure-side blow holes as described above must not be designed to be too large in order to minimize the return flow of already compressed medium in preceding working chambers (i.e., in lower-pressure working chambers). Such return flows increase the energy expenditure for the overall conveying capacity achieved and result in an undesirable increase in the temperature and pressure level during compression which overall reduces the efficiency. The area of the blow hole (blow hole area) can be kept small whereby the head roundings of the profiles in the transverse section are designed to be small. Specifically, this can be achieved by a strong curvature in the head region of the leading tooth flank of the secondary rotor and in the head region of the trailing tooth flank of the main rotor. However, the stronger is this curvature, the more rapidly production-technology limiting regions are reached since this for example results in high wear on profile millers and profile grinding disks during the manufacture of main rotor and secondary rotor.
Suction-side blow holes on the other hand do not have a negative influence on the energy efficiency since only working chambers in the suction region are interconnected via these at the same pressure.
Another cause of efficiency-reducing internal leakages is the so-called chamber interstitial volume which can form during expulsion of the last working chamber (i.e. the working chamber in which the highest pressure prevails) into the pressure window. The working chamber then no longer has a connection to the pressure window from a certain rotational angle position of the rotors. A so-called chamber interstitial volume remains between the two rotors and the pressure-side housing end wall.
This chamber interstitial volume is disadvantageous because the enclosed compressed medium can no longer be expelled into the pressure window and is even further compressed during the further rotation of the rotors, which leads to an unnecessarily high power consumption (for the over-compression), an unnecessarily high additional heat input, evolution of noise and a reduction in the lifetime, in particular of the roller bearings of the rotors. In addition, a deterioration in the specific power is caused by the fact that the fraction enclosed in the chamber interstitial volume is returned to the suction side after the over-compression and therefore is no longer available to the compressed air user. In the case of oil-injected compressors, incompressible oil is additionally in the chamber interstices and is squeezed.
2 Smooth Running
However, other properties such as, for example, the smooth running also have a decisive influence on a good profile for main rotor or secondary rotor.
In addition to good osculation of the flanks and low relative speeds between the tooth flanks of main and secondary rotor, the division of the drive torque between the two rotors also has a decisive influence on the two rotors. An unfavourable distribution is known to frequently result in so-called rotor rattling of the secondary rotor in which the secondary rotor has undefined flank contact with the main rotor and the secondary rotor consequently alternately has contact with the leading and the trailing main rotor flank. If the two rotors are held at a distance by means of a synchronous transmission, the aforesaid rotor rattling is necessarily displaced into the synchronous transmission. Good smooth running not only ensures low sound emissions from the compressor block but for example also provides for a less vibration-prone compressor block, a long lifetime of the roller bearings and low wear in the tooth structure of the rotors.
3 Costs
In particular, the manufacturability and the degree of utilization of the installation volume have an effect on the material and manufacturing costs of screw compressor blocks.
Compact compressor blocks with a high utilization of installation volume are achieved by a large tooth gap volume which in turn depends on the profile depth and the tooth thickness.
The further the relative profile depth is increased, the higher utilization of installation volume is achieved but at the same time, the risk of problems with running properties and manufacturability is higher:                With increasing profile depth, in particular the tooth profiles of the secondary rotor will necessarily become increasingly thinner and consequently increasingly flexible. This makes the rotors increasingly temperature-sensitive and when viewed overall, has an unfavourable effect on the gaps in the compressor block. The gaps have an appreciable influence on the internal leakages, i.e. return flows from higher-pressure compression chambers in the direction of the suction side, and can thus cause a deterioration in the energy efficiency of the compressor block.        Furthermore, in the case of flexible teeth the difficulties with rotor manufacture increase.                    Thus for example, there is an increased risk that the requirements in particular for the shape tolerances, which are already high in any case, cannot be adhered to.            Furthermore, flexible teeth require lower feed and intersection speeds both during profile milling and also during subsequent profile grinding and thus increase the processing time and consequently the manufacturing costs.                        An increasing profile depth also has the result that the rotor per se becomes more flexible. The more flexible the rotors are designed, the more the risk increases that the rotors start running amongst one another or in the compressor housing. In order to ensure operating safety even at high temperatures or at high pressures, the gaps must consequently have larger dimensions. This in turn has a negative influence on the energy efficiency of the compressor block.        